STRUCTURAL RELATION BETWEEN A 2D FIVEFOLD QUASI-CRYSTAL AND CRYSTALLINE APPROXIMANTS IN AN AL-CO-NI-TB ALLEY

A two-dimensional quasicrystal with fivefold symmetry and two large-un it-cell crystalline approximants in an Al-Co-Ni-Tb alloy, which were o bserved in previous studies, are suggested to be composed of the same kind of atom cluster. Some characteristics of the atom cluster can be deduced from a high-resolution electron microscopy image of the AI-Co- Ni-Tb quasicrystal when the image is associated with a fivefold aperio dic tiling. By using the cut-and-projection method, a quasiperiodic ti ling generated by an irrational projection is proposed as an ideal qua silattice of the Al-Co-Ni-Tb quasicrystal; in the meantime, periodic t ilings generated by a rational projection present the lattices of the crystalline approximants.